Prior Analytics - Book I   

belongs to no C. Suppose that it cannot belong, and that B belongs

to C, as above. It is necessary then that A belongs to some B: for

we have a syllogism in the third figure: but this is impossible.

Thus it will be possible for A to belong to no C; for if at is

supposed false, the consequence is an impossible one. This syllogism

then does not establish that which is possible according to the

definition, but that which does not necessarily belong to any part

of the subject (for this is the contradictory of the assumption

which was made: for it was supposed that A necessarily belongs to some

C, but the syllogism per impossibile establishes the contradictory

which is opposed to this). Further, it is clear also from an example

that the conclusion will not establish possibility. Let A be

'raven', B 'intelligent', and C 'man'. A then belongs to no B: for

no intelligent thing is a raven. But B is possible for all C: for

every man may possibly be intelligent. But A necessarily belongs to no

C: so the conclusion does not establish possibility. But neither is it

always necessary. Let A be 'moving', B 'science', C 'man'. A then will

belong to no B; but B is possible for all C. And the conclusion will

not be necessary. For it is not necessary that no man should move;

rather it is not necessary that any man should move. Clearly then

the conclusion establishes that one term does not necessarily belong

to any instance of another term. But we must take our terms better.

If the minor premiss is negative and indicates possibility, from the

actual premisses taken there can be no syllogism, but if the

problematic premiss is converted, a syllogism will be possible, as

before. Let A belong to all B, and let B possibly belong to no C. If

the terms are arranged thus, nothing necessarily follows: but if the

proposition BC is converted and it is assumed that B is possible for

all C, a syllogism results as before: for the terms are in the same

relative positions. Likewise if both the relations are negative, if

the major premiss states that A does not belong to B, and the minor

premiss indicates that B may possibly belong to no C. Through the